Chaotic Motions And Controlling Chaos In Dynamic Systems

Chaos exists and acts an important role in many engineering application and scientific research. It becomes more and more important to controlling chaos. Although studies on the controlling chaos have made a rapid progress since 1990s, the exploration on the methods of controlling chaos still stay at the early stage and there are many problem to be resolved. In this dissertation, the studies are carried out on two aspects: extending the chaos window and suppressing chaos.In the first part, an extended form of the stochastic Melnikov method is presented and applied in analysis on the homoclinic bifurcation and chaotic behavior of a nonlinear Hamiltonian system with weakly feed-back control and with both harmonic and Gaussian white noisy excitations. Numerical simulation is used to test the form and the results agree well with the theory, which proves the rationality of the form. The results reveal that the addition of stochastic excitation can make the parameter threshold value for the rising of the chaotic motions vary in a wider region, and so, the chaotic motions will appear easily in the system.In the second part, the chaos suppression is studied. In discrete dynamical systems, a new OGY strategy with new control start condition and feed-back control parameters is proposed. According to the new strategy, the chaotic motions of a Bloch wall, which is located in the zy plane experienced the action of an alternating external magnetic field, are analyzed and controlled. The results show that the chaotic motions of the Bloch wall are suppressed successfully, that is, the new strategy is successful and effective.In a time-continuous dynamical system, a new optimal control scheme is proposed base on the Krasovskii theory and is utilized to control the chaos in the Newton-Leipnik system which has double strange attractors. It is found that the N-L system can converge onto a selected fixed point rapidly and perfectly through asymptotic mode. Compared with a bang-bang control method, more effective control and flexible choice on control target are shown with the present scheme.The innovation of the present dissertation can be shown on three aspects. One is the stochastic extended form of the high-dimension Melnikov method which make it possible to choose proper noise excitation to extend the chaos window of a dynamical system. The following one is a new OGY strategy proposed by a new linearization method used in the neighborhood of fixed points, which provide a easy and effective way to control chaos in a discrete dynamical system. The last one is a new optimal control method based on Krasovskii theory, which makes it possible to drive and change the state of a system easily and control the chaotic motions of a system effectively.